We prove that there exists an integer p₀ such that X split (p)(ℚ) is made of cusps and CM-
points for any prime p> p₀. Equivalently, for any non-CM elliptic curve E over ℚ and any …

Let S_\mathbb Q (d) be the set of primes p for which there exists a number field K of degree
≤ d and an elliptic curve E/\mathbb Q, such that the order of the torsion subgroup of E (K) is …

We give a survey of a variety of recent results about the distribution and some geometric
properties of points (x, y) on modular hyperbolas xy ≡ a\;(\mod m). We also outline a very …

Using a multidimensional large sieve inequality, we obtain a bound for the mean-square
error in the Chebotarev theorem for division fields of elliptic curves that is as strong as what …

Let k be a field not of characteristic two, and let Λ be a set consisting of almost all rational
primes invertible in k. Suppose that we have a variety X/k and strictly compatible system {M …

Let E be an elliptic curve over QQ, and let n ≥ 1 n≥ 1. The central object of study of this
article is the division field Q (E n) Q (E n) that results by adjoining to QQ the coordinates of all …

Let k be an algebraically closed field of characteristic p. Let X (p^ e; N) be the curve
parameterizing elliptic curves with full level N structure (where p does not divide N) and full …

Let be a finite field whose characteristic is relatively prime to and. Let be a prime number that
is coprime to. Let be an elliptic curve over the global function field such that contains the …

In this paper, we give a survey and discuss new developments and computational results for
a high order accurate numerical boundary condition based on finite difference methods for …

Given an elliptic curve E over a number field k, the Galois action on the torsion points of E
induces a Galois representation ρE: Gal (k̄/k)→ GL2 (ℤ̂) For a fixed number field k, we …